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arXiv:0706.1228 · Journal of Modern Optics

Quantum information technology with Sagnac interferometer: interaction-free measurement, quantum key distribution and quantum secret sharing

Wellington Alves de Brito, Rubens Viana Ramos

Published May 10, 2008• 8 citations
arXivHTMLPDF

Abstract

The interferometry of single-photon pulses has been used to implement quantum technology systems, like quantum key distribution, interaction-free measurement and some other quantum communication protocols. In most of these implementations, Mach–Zehnder, Michelson and Fabry–Pérot interferometers are the most used. In this work we present optical setups for interaction-free measurement, quantum key distribution, quantum secret sharing and secure classical prisoners' dilemma game using the Sagnac interferometer. The proposed setups are described and as well the quantum protocols using them are explained.

DOI
10.1080/09500340701633113

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This work is divided into two parts. In the first one, the use of the Sagnac interferometer in quantum information is analyzed applying it in three problems: interaction-free measurement, quantum key distribution, and secret sharing. For the interaction-free measurement two systems using Sagnac interferometer were proposed. Considering ideal detectors and loss less devices, one of them has a success probability of 25% for each photon used while the other presents the probability of getting success to detect the presence of the object close to 100% for each photon used. For quantum key distribution, it was proposed a different setup, where the main difference is that the pulse sent by the transmitter does not come back to him/her as happen with the systems based on Sagnac proposed before. This avoids the Trojan horse attack. Finally, it was proposed an optical configuration where it is possible to share a secret among five users, locally distant, that could be used only when all five persons agreed. The second part of this dissertation presents an analytical and numerical study of the entanglement variation of bipartite states of qubits during propagation in a quantum noisy channel. Particularly, it was found an exactly formula which relates the entanglement of states in the input and output of the channel, when the input state is pure and the channel is modeled by a canonical unitary operation.

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The interferometry of single-photon pulses has been used to implement quantum technology systems, like quantum key distribution, interaction-free measurement and some other quantum communication protocols. In most of these implementations, Mach–Zehnder, Michelson and Fabry–Pérot interferometers are the most used. In this work we present optical setups for interaction-free measurement, quantum key distribution, quantum secret sharing and secure classical prisoners' dilemma game using the Sagnac interferometer. The proposed setups are described and as well the quantum protocols using them are explained.
This work is divided into two parts. In the first one, the use of the Sagnac interferometer in quantum information is analyzed applying it in three problems: interaction-free measurement, quantum key distribution, and secret sharing. For the interaction-free measurement two systems using Sagnac interferometer were proposed. Considering ideal detectors and loss less devices, one of them has a success probability of 25% for each photon used while the other presents the probability of getting success to detect the presence of the object close to 100% for each photon used. For quantum key distribution, it was proposed a different setup, where the main difference is that the pulse sent by the transmitter does not come back to him/her as happen with the systems based on Sagnac proposed before. This avoids the Trojan horse attack. Finally, it was proposed an optical configuration where it is possible to share a secret among five users, locally distant, that could be used only when all five persons agreed. The second part of this dissertation presents an analytical and numerical study of the entanglement variation of bipartite states of qubits during propagation in a quantum noisy channel. Particularly, it was found an exactly formula which relates the entanglement of states in the input and output of the channel, when the input state is pure and the channel is modeled by a canonical unitary operation.
We present the first Sagnac quantum secret sharing (in three- and four-party implementations) as well as Sagnac two-user quantum key distribution (QKD) over 1550 nm single mode fiber (SMF) networks, using the BB84- protocol with phase encoding. The secret sharing experiment has implemented a single qubit protocol, which allows for a practical secret sharing implementation over fiber telecom channels and in free-space. The previous quantum secret sharing proposals were based on multiparticle entangled states, not scalable and diffcult in the experimental implementations. Our experimental data show stable, in regards to birefringence drift, quantum secret sharing transmissions at the total Sagnac transmission loop distances of 45-55 km with the quantum bit error rates (QBER) of 3.0-3.7 % for the mean photon number μ = 0.1. In the QKD experiment we have achieved the total Sagnac transmission loop distances of 100-150 km with quantum bit error rates (QBER) of 5.84-9.79 % for μ = 0.1. The distances were much longer and rates much higher than in any other published Sagnac QKD experiments. The stability of quantum transmission in both secret sharing and QKD experiments has been achieved thanks to our new concept for compensation of SMF birefringence effects in Sagnac, based on a polarization control system and a polarization insensitive phase modulator. The measurement results have showed feasibility of quantum secret sharing and QKD over telecom fiber networks in Sagnac confi;guration, using standard fiber telecom components. Our birefringence compensation in SMF Sagnac open the door to other Sagnac-based applications over SMF links such as precise optical sensing, dispersion characteristics of optical fibers, acoustic and strain sensing, and generally sensing of any time varying phenomenon.
We are currently experiencing a rapid development of quantum information, a new branch of science, being an interdisciplinary of quantum physics, information theory, telecommunications, computer science, and many others. This new science branch was born in the middle of the eighties, developed rapidly during the nineties, and in the current decade has brought a technological breakthrough in creating secure quantum key distribution (QKD), quantum secret sharing, and exciting promises in diverse technological fields. Recent QKD experiments have achieved high rate QKD at 200 km distance in optical fiber. Significant QKD results have also been achieved in free-space. Due to the rapid broadband access deployment in many industrialized countries and the standing increasing transmission security treats, the natural development awaiting quantum communications, being a part of quantum information, is its migration into commercial switched telecom networks. Such a migration concerns both multiuser quantum key distribution and multiparty quantum secret sharing that have been the main goal of my PhD studies. They are also the main concern of the thesis. Our research efforts in multiuser QKD has led to a development of the five-user setup for transmissions over switched fiber networks in a star and in a tree configuration. We have achieved longer secure quantum information distances and implemented more nodes than other multi-user QKD experiments. The measurements have shown feasibility of multiuser QKD over switched fiber networks, using standard fiber telecom components. Since circular architecture networks are important parts of both intranets and the Internet, Sagnac QKD has also been a subject of our research efforts. The published experiments in this area have been very few and results were not encouraging, mainly due to the single mode fiber (SMF) birefringence. Our research has led to a development of a computer controlled birefringence compensation in Sagnac that open the door to both classical and quantum Sagnac applications. On the quantum secret sharing side, we have achieved the first quantum secret sharing experiment over telecom fiber in a five-party implementation using the "plug & play" setup and in a four-party implementation using Sagnac configuration. The setup measurements have shown feasibility and scalability of multiparty quantum communication over commercial telecom fiber networks.
We report the first Sagnac quantum secret sharing (in three-and four-party implementations) over 1550 nm single mode fiber (SMF) networks, using a single qubit protocol with phase encoding. Our secret sharing experiment has been based on a single qubit protocol, which has opened the door to practical secret sharing implementation over fiber telecom channels and in free-space. The previous quantum secret sharing proposals were based on multiparticle entangled states, difficult in the practical implementation and not scalable. Our experimental data in the three-party implementation show stable (in regards to birefringence drift) quantum secret sharing transmissions at the total Sagnac transmission loop distances of 55-75 km with the quantum bit error rates (QBER) of 2.3-2.4% for the mean photon number micro?= 0.1 and 1.7-2.1% for micro= 0.3. In the four-party case we have achieved quantum secret sharing transmissions at the total Sagnac transmission loop distances of 45-55 km with the quantum bit error rates (QBER) of 3.0-3.7% for the mean photon number micro= 0.1 and 1.8-3.0% for micro?= 0.3. The stability of quantum transmission has been achieved thanks to our new concept for compensation of SMF birefringence effects in Sagnac, based on a polarization control system and a polarization insensitive phase modulator. The measurement results have showed feasibility of quantum secret sharing over telecom fiber networks in Sagnac configuration, using standard fiber telecom components.
Quantum key distribution, which allows two distant parties to share an unconditionally secure cryptographic key, promises to play an important role in the future of communication. For this reason such technique has attracted many theoretical and experimental efforts, thus becoming one of the most prominent quantum technologies of the last decades. The security of the key relies on quantum mechanics and therefore requires the users to be capable of performing quantum operations, such as state preparation or measurements in multiple bases. A natural question is whether and to what extent these requirements can be relaxed and the quantum capabilities of the users reduced. Here we demonstrate a novel quantum key distribution scheme, where users are fully classical. In our protocol, the quantum operations are performed by an untrusted third party acting as a server, which gives the users access to a superimposed single photon, and the key exchange is achieved via interaction-free measurements on the shared state. We also provide a full security proof of the protocol by computing the secret key rate in the realistic scenario of finite-resources, as well as practical experimental conditions of imperfect photon source and detectors. Our approach deepens the understanding of the fundamental principles underlying quantum key distribution and, at the same time, opens up new interesting possibilities for quantum cryptography networks
Quantum information and quantum optics offer powerful innovative tools for secure communication and cryptography, with Quantum Key Distribution (QKD) becoming a standard technology in the cryptographic world. By exploiting fundamental principles such as quantum superposition, entanglement, and the no-cloning theorem, QKD enables two users to establish a shared secret key with information-theoretic security. Quantum communication is a fundamental element for the realization of the quantum internet, a network of distant nodes connected by quantum channel. The realization of such networks requires methods to distribute states and correlations with high fidelity and low losses. This thesis explores the use of innovative photonic technologies for the realization of experiment aiming at improving quantum communication and quantum channels. Single photons based on QD are generated on-demand and show high purity, near-optimal indistinguishability and low multi-photons emission. By exploiting the features of these photons, a method to realize entangled states is implemented. Using the polarization degree of freedom, these entangled states are ideal candidates for free-space QKD protocols based on the Bell’s inequality. To address the problem of the reference frame alignment using the polarization, hybrid states are studied and implemented. The specific combination of polarization and orbital angular momentum (OAM) can produce photons that are not modified by rotation of the reference frame. We implemented an experiment to realize a QKD that is independent on the relative rotation of the two user. The final goal of my thesis was devoted to the in-field demonstration of quantum teleportation as a fundamental building block of distributed quantum networks, enabling the reliable transmission of quantum information between remote nodes. Exploiting the free-space infrastructure in the "Sapienza" University of Rome, a link of around ∼ 300 m, we implemented the quantum teleportation between two different QDs showing the possibility of using this technology into real-case scenario. The results obtained show not only that QDs are ideal sources for quantum communication, but also the possibility of using new states to improve current technologies, advancing the development of efficient and reliable quantum networks.